Solve 3/x+5=4/1-2x

$$\frac { 3 } { x + 5 } = \frac { 4 } { 1 - 2 x }$$

Solve for x

$$x = -\frac{17}{10} = -1\frac{7}{10} = -1.7$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x-1\right)\left(x+5\right), the least common multiple of x+5,1-2x.

$$\left(2x-1\right)\times 3=-\left(5+x\right)\times 4$$

Use the distributive property to multiply 2x-1 by 3.

$$6x-3=-\left(5+x\right)\times 4$$

Multiply -1 and 4 to get -4.

$$6x-3=-4\left(5+x\right)$$

Use the distributive property to multiply -4 by 5+x.

$$6x-3=-20-4x$$

Add 4x to both sides.

$$6x-3+4x=-20$$

Combine 6x and 4x to get 10x.

$$10x-3=-20$$

Add 3 to both sides.

$$10x=-20+3$$

Add -20 and 3 to get -17.

$$10x=-17$$

Divide both sides by 10.

$$x=\frac{-17}{10}$$

Fraction \frac{-17}{10} can be rewritten as -\frac{17}{10} by extracting the negative sign.

$$x=-\frac{17}{10}$$